{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tracking an Unknown Number of Objects\n",
    "\n",
    "While SVI can be used to learn components and assignments of a mixture model, pyro.contrib.tracking provides more efficient inference algorithms to estimate assignments. This notebook demonstrates how to use the `MarginalAssignmentPersistent` inside SVI."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import os\n",
    "import torch\n",
    "from torch.distributions import constraints\n",
    "from matplotlib import pyplot\n",
    "\n",
    "import pyro\n",
    "import pyro.distributions as dist\n",
    "import pyro.poutine as poutine\n",
    "from pyro.contrib.tracking.assignment import MarginalAssignmentPersistent\n",
    "from pyro.distributions.util import gather\n",
    "from pyro.infer import SVI, TraceEnum_ELBO\n",
    "from pyro.optim import Adam\n",
    "\n",
    "%matplotlib inline\n",
    "assert pyro.__version__.startswith('1.5.1')\n",
    "pyro.enable_validation(True)\n",
    "smoke_test = ('CI' in os.environ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's consider a model with deterministic dynamics, say sinusoids with known period but unknown phase and amplitude."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_dynamics(num_frames):\n",
    "    time = torch.arange(float(num_frames)) / 4\n",
    "    return torch.stack([time.cos(), time.sin()], -1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's tricky to define a fully generative model, so instead we'll separate our data generation process `generate_data()` from a factor graph `model()` that will be used in inference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_data(args):\n",
    "    # Object model.\n",
    "    num_objects = int(round(args.expected_num_objects))  # Deterministic.\n",
    "    states = dist.Normal(0., 1.).sample((num_objects, 2))\n",
    "\n",
    "    # Detection model.\n",
    "    emitted = dist.Bernoulli(args.emission_prob).sample((args.num_frames, num_objects))\n",
    "    num_spurious = dist.Poisson(args.expected_num_spurious).sample((args.num_frames,))\n",
    "    max_num_detections = int((num_spurious + emitted.sum(-1)).max())\n",
    "    observations = torch.zeros(args.num_frames, max_num_detections, 1+1) # position+confidence\n",
    "    positions = get_dynamics(args.num_frames).mm(states.t())\n",
    "    noisy_positions = dist.Normal(positions, args.emission_noise_scale).sample()\n",
    "    for t in range(args.num_frames):\n",
    "        j = 0\n",
    "        for i, e in enumerate(emitted[t]):\n",
    "            if e:\n",
    "                observations[t, j, 0] = noisy_positions[t, i]\n",
    "                observations[t, j, 1] = 1\n",
    "                j += 1\n",
    "        n = int(num_spurious[t])\n",
    "        if n:\n",
    "            observations[t, j:j+n, 0] = dist.Normal(0., 1.).sample((n,))\n",
    "            observations[t, j:j+n, 1] = 1\n",
    "\n",
    "    return states, positions, observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(args, observations):\n",
    "    with pyro.plate(\"objects\", args.max_num_objects):\n",
    "        exists = pyro.sample(\"exists\",\n",
    "                             dist.Bernoulli(args.expected_num_objects / args.max_num_objects))\n",
    "        with poutine.mask(mask=exists.bool()):\n",
    "            states = pyro.sample(\"states\", dist.Normal(0., 1.).expand([2]).to_event(1))\n",
    "            positions = get_dynamics(args.num_frames).mm(states.t())\n",
    "    with pyro.plate(\"detections\", observations.shape[1]):\n",
    "        with pyro.plate(\"time\", args.num_frames):\n",
    "            # The combinatorial part of the log prob is approximated to allow independence.\n",
    "            is_observed = (observations[..., -1] > 0)\n",
    "            with poutine.mask(mask=is_observed):\n",
    "                assign = pyro.sample(\"assign\",\n",
    "                                     dist.Categorical(torch.ones(args.max_num_objects + 1)))\n",
    "            is_spurious = (assign == args.max_num_objects)\n",
    "            is_real = is_observed & ~is_spurious\n",
    "            num_observed = is_observed.float().sum(-1, True)\n",
    "            pyro.sample(\"is_real\",\n",
    "                        dist.Bernoulli(args.expected_num_objects / num_observed),\n",
    "                        obs=is_real.float())\n",
    "            pyro.sample(\"is_spurious\",\n",
    "                        dist.Bernoulli(args.expected_num_spurious / num_observed),\n",
    "                        obs=is_spurious.float())\n",
    "\n",
    "            # The remaining continuous part is exact.\n",
    "            observed_positions = observations[..., 0]\n",
    "            with poutine.mask(mask=is_real):\n",
    "                bogus_position = positions.new_zeros(args.num_frames, 1)\n",
    "                augmented_positions = torch.cat([positions, bogus_position], -1)\n",
    "                predicted_positions = gather(augmented_positions, assign, -1)\n",
    "                pyro.sample(\"real_observations\",\n",
    "                            dist.Normal(predicted_positions, args.emission_noise_scale),\n",
    "                            obs=observed_positions)\n",
    "            with poutine.mask(mask=is_spurious):\n",
    "                pyro.sample(\"spurious_observations\", dist.Normal(0., 1.),\n",
    "                            obs=observed_positions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This guide uses a smart assignment solver but a naive state estimator. A smarter implementation would use message passing also for state estimation, e.g. a Kalman filter-smoother."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def guide(args, observations):\n",
    "    # Initialize states randomly from the prior.\n",
    "    states_loc = pyro.param(\"states_loc\", lambda: torch.randn(args.max_num_objects, 2))\n",
    "    states_scale = pyro.param(\"states_scale\",\n",
    "                              lambda: torch.ones(states_loc.shape) * args.emission_noise_scale,\n",
    "                              constraint=constraints.positive)\n",
    "    positions = get_dynamics(args.num_frames).mm(states_loc.t())\n",
    "\n",
    "    # Solve soft assignment problem.\n",
    "    real_dist = dist.Normal(positions.unsqueeze(-2), args.emission_noise_scale)\n",
    "    spurious_dist = dist.Normal(0., 1.)\n",
    "    is_observed = (observations[..., -1] > 0)\n",
    "    observed_positions = observations[..., 0].unsqueeze(-1)\n",
    "    assign_logits = (real_dist.log_prob(observed_positions) -\n",
    "                     spurious_dist.log_prob(observed_positions) +\n",
    "                     math.log(args.expected_num_objects * args.emission_prob /\n",
    "                              args.expected_num_spurious))\n",
    "    assign_logits[~is_observed] = -float('inf')\n",
    "    exists_logits = torch.empty(args.max_num_objects).fill_(\n",
    "        math.log(args.max_num_objects / args.expected_num_objects))\n",
    "    assignment = MarginalAssignmentPersistent(exists_logits, assign_logits)\n",
    "\n",
    "    with pyro.plate(\"objects\", args.max_num_objects):\n",
    "        exists = pyro.sample(\"exists\", assignment.exists_dist, infer={\"enumerate\": \"parallel\"})\n",
    "        with poutine.mask(mask=exists.bool()):\n",
    "            pyro.sample(\"states\", dist.Normal(states_loc, states_scale).to_event(1))\n",
    "    with pyro.plate(\"detections\", observations.shape[1]):\n",
    "        with poutine.mask(mask=is_observed):\n",
    "            with pyro.plate(\"time\", args.num_frames):\n",
    "                assign = pyro.sample(\"assign\", assignment.assign_dist, infer={\"enumerate\": \"parallel\"})\n",
    "\n",
    "    return assignment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll define a global config object to make it easy to port code to `argparse`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "args = type('Args', (object,), {})  # A fake ArgumentParser.parse_args() result.\n",
    "\n",
    "args.num_frames = 5\n",
    "args.max_num_objects = 3\n",
    "args.expected_num_objects = 2.\n",
    "args.expected_num_spurious = 1.\n",
    "args.emission_prob = 0.8\n",
    "args.emission_noise_scale = 0.1\n",
    "\n",
    "assert args.max_num_objects >= args.expected_num_objects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "generated 16 detections from 2 objects\n"
     ]
    }
   ],
   "source": [
    "pyro.set_rng_seed(0)\n",
    "true_states, true_positions, observations = generate_data(args)\n",
    "true_num_objects = len(true_states)\n",
    "max_num_detections = observations.shape[1]\n",
    "assert true_states.shape == (true_num_objects, 2)\n",
    "assert true_positions.shape == (args.num_frames, true_num_objects)\n",
    "assert observations.shape == (args.num_frames, max_num_detections, 1+1)\n",
    "print(\"generated {:d} detections from {:d} objects\".format(\n",
    "    (observations[..., -1] > 0).long().sum(), true_num_objects))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_solution(message=''):\n",
    "    assignment = guide(args, observations)\n",
    "    states_loc = pyro.param(\"states_loc\")\n",
    "    positions = get_dynamics(args.num_frames).mm(states_loc.t())\n",
    "    pyplot.figure(figsize=(12,6)).patch.set_color('white')\n",
    "    pyplot.plot(true_positions.numpy(), 'k--')\n",
    "    is_observed = (observations[..., -1] > 0)\n",
    "    pos = observations[..., 0]\n",
    "    time = torch.arange(float(args.num_frames)).unsqueeze(-1).expand_as(pos)\n",
    "    pyplot.scatter(time[is_observed].view(-1).numpy(),\n",
    "                   pos[is_observed].view(-1).numpy(), color='k', marker='+',\n",
    "                   label='observation')\n",
    "    for i in range(args.max_num_objects):\n",
    "        p_exist = assignment.exists_dist.probs[i].item()\n",
    "        position = positions[:, i].detach().numpy()\n",
    "        pyplot.plot(position, alpha=p_exist, color='C0')\n",
    "    pyplot.title('Truth, observations, and predicted tracks ' + message)\n",
    "    pyplot.plot([], 'k--', label='truth')\n",
    "    pyplot.plot([], color='C0', label='prediction')\n",
    "    pyplot.legend(loc='best')\n",
    "    pyplot.xlabel('time step')\n",
    "    pyplot.ylabel('position')\n",
    "    pyplot.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyro.set_rng_seed(1)\n",
    "pyro.clear_param_store()\n",
    "plot_solution('(before training)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch    0 loss = 89.270072937\n",
      "epoch   10 loss = 85.940826416\n",
      "epoch   20 loss = 86.1014556885\n",
      "epoch   30 loss = 83.8865127563\n",
      "epoch   40 loss = 85.354347229\n",
      "epoch   50 loss = 82.01512146\n",
      "epoch   60 loss = 78.1765365601\n",
      "epoch   70 loss = 78.0290603638\n",
      "epoch   80 loss = 74.915725708\n",
      "epoch   90 loss = 74.3280792236\n",
      "epoch  100 loss = 74.1109313965\n"
     ]
    }
   ],
   "source": [
    "infer = SVI(model, guide, Adam({\"lr\": 0.01}), TraceEnum_ELBO(max_plate_nesting=2))\n",
    "losses = []\n",
    "for epoch in range(101 if not smoke_test else 2):\n",
    "    loss = infer.step(args, observations)\n",
    "    if epoch % 10 == 0:\n",
    "        print(\"epoch {: >4d} loss = {}\".format(epoch, loss))\n",
    "    losses.append(loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.plot(losses);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_solution('(after training)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
